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<title>算法提高 Monday-Saturday质因子</title>
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 <p class="MsoNormal" style="text-align: left; "><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">【题目描述】</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">这个问题是个简单的与数论有关的题目，看起来似乎是</span><span lang="EN-US">&ldquo;</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">求正整数的所有质因子</span><span lang="EN-US">&rdquo;</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">，但实际上并不完全是这样。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span lang="EN-US">&nbsp;</span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">本题中需要定义以下几个概念：</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:39.0pt;text-indent:-18.0pt;
mso-char-indent-count:0;mso-list:l0 level1 lfo1"><!--[if !supportLists]--><span lang="EN-US">1．<span style="font-size: 7pt; font-family: 'Times New Roman'; ">&nbsp; </span></span><!--[endif]--><span lang="EN-US">Monday-Saturday</span><span style="font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">数</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">对于一个正整数</span><span lang="EN-US">N</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">，如果它除以</span><span lang="EN-US">7</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">得到的余数是</span><span lang="EN-US">1</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">或</span><span lang="EN-US">6</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">，则可以写成</span><span lang="EN-US">N=7k+{1,6}</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">的形式。更形象的，我们把这样的</span><span lang="EN-US">N</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">称作</span><span lang="EN-US">&ldquo;Monday-Saturday</span><span style="font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">数</span><span lang="EN-US">&rdquo;</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">，简称</span><span lang="EN-US">&ldquo;MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">数</span><span lang="EN-US">&rdquo;</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:39.0pt;text-indent:-18.0pt;
mso-char-indent-count:0;mso-list:l0 level1 lfo1"><!--[if !supportLists]--><span lang="EN-US">2．<span style="font-size: 7pt; font-family: 'Times New Roman'; ">&nbsp; </span></span><!--[endif]--><span lang="EN-US">Monday-Saturday</span><span style="font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">因子</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">如果对于两个</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">数</span><span lang="EN-US">a,b</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">，若存在一个</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">数</span><span lang="EN-US">x</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">，使得</span><span lang="EN-US">ax=b</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">，那么就称</span><span lang="EN-US">a</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">是</span><span lang="EN-US">b</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">的一个</span><span lang="EN-US">&ldquo;Monday-Saturday</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">因子</span><span lang="EN-US">&rdquo;</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">，简称</span><span lang="EN-US">&ldquo;MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">因子</span><span lang="EN-US">&rdquo;</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:39.0pt;text-indent:-18.0pt;
mso-char-indent-count:0;mso-list:l0 level1 lfo1"><!--[if !supportLists]--><span lang="EN-US">3．<span style="font-size: 7pt; font-family: 'Times New Roman'; ">&nbsp; </span></span><!--[endif]--><span lang="EN-US">Monday-Saturday</span><span style="font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">质数</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">如果对于</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">数</span><span lang="EN-US">a</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">，满足</span><span lang="EN-US">a&gt;1</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">且除了</span><span lang="EN-US">1</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">和</span><span lang="EN-US">a</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">之外</span><span lang="EN-US">a</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">没有其他的</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">因子，那么称</span><span lang="EN-US">a</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">是一个</span><span lang="EN-US">&ldquo;Monday-Saturday</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">质数</span><span lang="EN-US">&rdquo;</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">，简称</span><span lang="EN-US">&ldquo;MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">质数</span><span lang="EN-US">&rdquo;</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">注：对于传统意义上的质数，若它是一个</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">数，则它一定是一个</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">质数。但反之不必成立，例如</span><span lang="EN-US">27</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">，它是一个</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">质数但不是传统意义上的质数。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:39.0pt;text-indent:-18.0pt;
mso-char-indent-count:0;mso-list:l0 level1 lfo1"><!--[if !supportLists]--><span lang="EN-US">4．<span style="font-size: 7pt; font-family: 'Times New Roman'; ">&nbsp; </span></span><!--[endif]--><span lang="EN-US">Monday-Saturday</span><span style="font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">质因子</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">如果对于两个</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">数</span><span lang="EN-US">a,b</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">，若满足</span><span lang="EN-US">a</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">是</span><span lang="EN-US">b</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">的</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">因子且</span><span lang="EN-US">a</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">是一个</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">质数，那么称</span><span lang="EN-US">a</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">是</span><span lang="EN-US">b</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">的一个</span><span lang="EN-US">&ldquo;Monday-Saturday</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">质因子</span><span lang="EN-US">&rdquo;</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">例如：</span><span lang="EN-US">27</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">是</span><span lang="EN-US">216</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">的一个</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">质因子（</span><span lang="EN-US">216=27*8</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">）。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span lang="EN-US">&nbsp;</span></p>
<p class="MsoNormal" style="text-indent:21.0pt;mso-char-indent-count:2.0"><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">问题就是，给定一个</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">数</span><span lang="EN-US">N</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">，求其所有的</span><span lang="EN-US">Monday-Saturday</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">质因子。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">&nbsp;</span></p>
<p class="MsoNormal"><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">【输入数据】</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt"><span style="font-family:宋体;
mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin">每个输入数据包含多行，每行一个整数</span><span lang="EN-US">N</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">（保证</span><span lang="EN-US">N</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">一定是</span><span lang="EN-US">MS</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">数，</span><span lang="EN-US">1</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">＜</span><span lang="EN-US">N</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">＜</span><span lang="EN-US">300000</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">）。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt"><span style="font-family:宋体;
mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin">输入的最后一行是一个整数</span><span lang="EN-US">1</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">（对于这一行，你不必输出任何信息）。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt"><span style="font-family:宋体;
mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin">每个输入数据不超过</span><span lang="EN-US">100</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">行。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">&nbsp;</span></p>
<p class="MsoNormal"><span style="font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">【输出数据】</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-indent:21.0pt"><span style="font-family:宋体;
mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin">对于每个</span><span lang="EN-US">N</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">输出一行，表示</span><span lang="EN-US">N</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">的所有</span><span lang="EN-US">Monday-Saturday</span><span style="font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin">质因子，按从小到大的顺序输出。格式形如</span><span lang="EN-US">&ldquo;N: p1 p2 p3 &hellip;&hellip; pk&rdquo;</span><span style="font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">，注意行末无多余空格。</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">&nbsp;</span></p>
<p class="MsoNormal"><b><span lang="EN-US">【样例输入】</span></b><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">205920<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">262144<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">262200<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">279936<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">299998<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">1<o:p></o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US">&nbsp;</span></b></p>
<p class="MsoNormal"><b><span lang="EN-US">【样例输出】</span></b><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">205920: 6 8 13 15 20 22 55 99<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">262144: 8<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">262200: 6 8 15 20 50 57 69 76 92 190 230 475 575 874 2185<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">279936: 6 8 27<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">299998: 299998</span></p>
<p class="MsoNormal">&nbsp;</p>
<p class="MsoNormal">【数据规模和约定】</p>
<p class="MsoNormal"><span lang="EN-US" style="text-indent: 28px; ">1</span><span style="text-indent: 28px; font-family: 宋体; ">＜</span><span lang="EN-US" style="text-indent: 28px; ">N</span><span style="text-indent: 28px; font-family: 宋体; ">＜</span><span lang="EN-US" style="text-indent: 28px; ">300000，</span><span style="text-indent: 28px; font-family: 宋体; ">每个输入数据不超过</span><span lang="EN-US" style="text-indent: 28px; ">100</span><span style="text-indent: 28px; font-family: 宋体; ">行。</span></p>